1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
16 **************************************************************************/
20 // This class performs a fast fit of helices going through the <=6 *
21 // points of the ITS, with the goal of studying tracking and *
22 // vertexing performances. *
23 // Generated kinematics is used to take into account different weights *
24 // associated to points in different layers (with different multiple *
25 // scattering-originated errors). *
27 // Based on the work by A. Strandlie, R. Fruhwirth *
29 // First implementation by N. Bustreo, R. Turrisi - July 2000 *
31 // Further modifications by A. Dainese, R. Turrisi *
33 // Contact: Rosario Turrisi, rosario.turrisi@pd.infn.it *
35 // ************************************************************************
38 // Modified November, 7th 2001 by Rosario Turrisi
39 // (rosario.turrisi@pd.infn.it)
41 // FitHelix returns different values. 0=ok, >0 =problem
42 // void FitLinear -> Int_t FitLinear to give feedback of errors to FitHelix
45 // Modified July, 30th 2001 by Rosario Turrisi
46 // (rosario.turrisi@pd.infn.it)
48 // Fit for z now in (z,s) plane.
49 // Returns parameters in order to write the helix equation
50 // and find the right phase/initial point.
52 // "PROPER WEIGHTS": (1+R^2)^2/(\sigma_x^2 + \sigma_y^2 + \sigma_MS^2)
57 #include "AliITSRiemannFit.h"
59 #include "TClonesArray.h"
62 #include "Riostream.h"
64 #include "TGraphErrors.h"
65 #include "TParticle.h"
68 #include "AliITSRecPoint.h"
69 #include "AliITSgeom.h"
71 #include "AliITSDetTypeRec.h"
74 ClassImp(AliITSRiemannFit)
77 AliITSRiemannFit::AliITSRiemannFit() {
78 ///////////////////////////////////////////////////////////
79 // Default constructor.
80 // Set everything to zero.
81 ////////////////////////////////////////////////////////////
91 for(Int_t i=0;i<6;i++)fPLay[i] = 0;
95 //______________________________________________________________________
96 AliITSRiemannFit::AliITSRiemannFit(const AliITSRiemannFit &rf) : TObject(rf) {
98 // Copies are not allowed. The method is protected to avoid misuse.
99 Error("AliITSRiemannFit","Copy constructor not allowed\n");
102 //______________________________________________________________________
103 AliITSRiemannFit& AliITSRiemannFit::operator=(const AliITSRiemannFit& /* rf */){
104 // Assignment operator
105 // Assignment is not allowed. The method is protected to avoid misuse.
106 Error("= operator","Assignment operator not allowed\n");
110 //______________________________________________________________________
111 AliITSRiemannFit::~AliITSRiemannFit() {
112 ///////////////////////////////////////////////////////////
113 // Default destructor.
114 // if arrays exist delete them. Then set everything to zero.
115 ////////////////////////////////////////////////////////////
117 for(Int_t i=0;i<fSizeEvent;i++) delete[] fPointRecs[i];
119 } // end if fPointRecs!=0
128 for(Int_t i=0;i<6;i++)fPLay[i] = 0;
131 //----------------------------------------------------------------------
133 AliITSRiemannFit::AliITSRiemannFit(Int_t size,Int_t ntracks) {
134 ///////////////////////////////////////////////////////////
136 // Set fSizeEvent to size and fPrimaryTracks to ntracks.
138 ////////////////////////////////////////////////////////////
142 fPrimaryTracks = ntracks;
147 AliPointtl *first = new AliPointtl[fSizeEvent];
148 AliPointtl **pointRecs = new AliPointtl*[fSizeEvent];
149 for(Int_t i=0;i<6;i++)fPLay[i] = 0;
150 for(Int_t j=0;j<fSizeEvent;j++) // create an array of struct
151 pointRecs[j] = &(first[j]);
154 // ---------------------------------------------------------------------
155 AliITSRiemannFit::AliPointtl::AliPointtl(){
156 // default constructor
179 // ---------------------------------------------------------------------
181 void FillPoints(AliITSRiemannFit::AliPointtl **Points,Int_t &index,Float_t *xpoint,
183 TLorentzVector pE,TLorentzVector oT,Int_t *id,
184 Int_t track, Char_t *name,Int_t code,
186 ///////////////////////////////////////////////////////////////////////
187 // Fill the structure AliPointtl with the proper data
189 //////////////////////////////////////////////////////////////////////
190 Float_t pPI2 = 2.0*TMath::Pi();
198 phi = TMath::ATan2(y,x);
199 if(phi<0.0) phi += pPI2;
200 Points[i]->SetPhi(phi);
201 Points[i]->SetEta(-0.5*tan(0.5*TMath::ATan2(r,z)));
205 Points[i]->SetdX(error[0]);
206 Points[i]->SetdY(error[1]);
207 Points[i]->SetdZ(error[2]);
209 Points[i]->SetTrack(track);
210 Points[i]->SetLay(id[0]);
211 Points[i]->SetLad(id[1]);
212 Points[i]->SetDet(id[2]);
213 Points[i]->SetMomentum(&pE);
214 Points[i]->SetOrigin(&oT);
215 Points[i]->SetPt(sqrt(pE.X()*pE.X()+pE.Y()*pE.Y()));
216 Points[i]->SetCode(code);
217 Points[i]->SetName(name);
218 Points[i]->SetVertexPhi(phiorigin);
223 // -----------------------------------------------------------------------
225 void AliITSRiemannFit::InitPoints(Int_t ntracks,TTree *TR,Int_t nparticles){
226 //////////////////////////////////////////////////////////////////////
227 // Fill the class member fPointRecs with the reconstructed points
228 // Set All other members to the real values
230 /////////////////////////////////////////////////////////////////////
231 printf("\n ************* Starting Init Points *************\n");
234 AliRunLoader* rl = AliRunLoader::Open("galice.root");
236 AliITSLoader* loader = static_cast<AliITSLoader*>(rl->GetLoader("ITSLoader"));
238 Error("InitPoints", "ITS loader not found");
241 AliITSgeom* gm = loader->GetITSgeom();
243 //get pointer to modules array
244 Int_t nmodules = gm->GetIndexMax();
245 // Get the points from points file
248 AliITSRecPoint *recp;
249 nent=TR->GetEntries();
250 AliITSDetTypeRec detTypeRec;
251 TClonesArray *iTSrec = detTypeRec.RecPoints();
253 for (mod=0; mod<nmodules; mod++) {
254 detTypeRec.ResetRecPoints();
256 Int_t nrecp = iTSrec->GetEntries();
262 fPrimaryTracks = ntracks;
263 fParticles = nparticles;
264 AliITSRiemannFit::AliPointtl *global = new AliPointtl[iMAX];
265 fPointRecs = new AliITSRiemannFit::AliPointtl*[iMAX];
267 for(Int_t j=0;j<iMAX;j++) {
268 fPointRecs[j] = &(global[j]);
271 Int_t ieta=0,ieta2=0;
272 Int_t i,id[4],idold[4];
273 Int_t track=0;// // track of hit
274 Float_t xpoint[3],errorPlus[3],errorMinus[3],globalError[3]; // position and error of the point
275 TLorentzVector oT,pE;
276 Float_t locals[3],localserror[3],localsplus[3],localsminus[3]; // local position and local errors
280 Int_t layer,ladder,detector;
281 Float_t xcluster,zcluster;
282 Int_t num=0,nspdi=0,nspdo=0,nsddi=0,nsddo=0,nssdi=0,nssdo=0;
284 for (mod=0; mod<nmodules; mod++) {
285 //itsModule=(AliITSmodule*)iTSmodules->At(mod);
286 //ITS->ResetRecPoints();
287 detTypeRec.ResetRecPoints();
289 Int_t nrecp = iTSrec->GetEntries();
290 if (!nrecp) continue;
291 //itsModule->GetID(layer,ladder,detector);
292 gm->GetModuleId(mod,layer,ladder,detector);
294 for (irec=0;irec<nrecp;irec++) {
295 recp = (AliITSRecPoint*)iTSrec->UncheckedAt(irec);
296 track=recp->GetLabel(0);
297 if(track <0 ) continue;
298 xcluster=recp->GetDetLocalX(); // x on cluster
299 zcluster=recp->GetDetLocalZ(); // z on cluster
300 part = (TParticle*) gAlice->GetMCApp()->Particle(track);
301 part->ProductionVertex(oT); // set the vertex
302 part->Momentum(pE); // set the vertex momentum
303 name = part->GetName();
305 sprintf(nam2,"%s",name);
306 code = part->GetPdgCode();
312 locals[0]=xcluster; // x on cluster
313 locals[1]=0.0; // y on cluster
314 locals[2]=zcluster; // z on cluster
315 localserror[0]=sqrt(recp->GetSigmaDetLocX2());
317 localserror[2]=sqrt(recp->GetSigmaZ2());
318 localsplus[0]=xcluster+sqrt(recp->GetSigmaDetLocX2()); // x on cluster
319 if(layer==1||layer==2) localsplus[1]=0.0150/2; // y on cluster
320 else if(layer==3||layer==4) localsplus[1]=0.0280/2; // y on cluster
321 else if(layer==5||layer==6) localsplus[1]=0.0300/2; // y on cluster
322 localsplus[2]=zcluster+sqrt(recp->GetSigmaZ2()); // z on cluster
323 localsminus[0]=xcluster-sqrt(recp->GetSigmaDetLocX2()); // x on cluster
324 localsminus[1]=0.0; // y on cluster
325 localsminus[2]=zcluster-sqrt(recp->GetSigmaZ2()); // z on cluster
327 gm->LtoG(layer,ladder,detector,locals,xpoint);
328 gm->LtoG(layer,ladder,detector,localsplus,errorPlus);
329 gm->LtoG(layer,ladder,detector,localsminus,errorMinus);
330 globalError[0]=0.5*TMath::Abs(errorPlus[0]-errorMinus[0]);
331 globalError[1]=0.5*TMath::Abs(errorPlus[1]-errorMinus[1]);
332 globalError[2]=0.5*TMath::Abs(errorPlus[2]-errorMinus[2]);
334 if(TMath::Abs(part->Eta())<=1.0) ieta++;
335 if(TMath::Abs(part->Eta())<=0.5) ieta2++;
337 if(!(id[0]==idold[0]&&id[1]==idold[1]&&
338 id[2]==idold[2]&&id[3]==idold[3])) {
339 FillPoints(fPointRecs,num,xpoint,globalError,pE,oT,id,track,nam2,code,pPhi);
363 // FillPoints(fspdi,nspdi,xpoint,globalError,pE,oT,id,track,name,code,pPhi);
367 // FillPoints(fspdo,nspdo,xpoint,globalError,pE,oT,id,track,name,code,pPhi);
381 for(i=0;i<4;i++) idold[i] = id[i];
382 for(i=0;i<3;i++) xpoint[i] = 0.0;
383 } // end if id != idold
397 printf("%d primary tracks in eta=+-1\n",ieta);
398 printf("%d primary tracks#2 in eta=+-0.5\n",ieta2);
399 printf("\nInitPoints :\n\nPoints on Layer1 : %d on Layer2 : %d\n",nspdi,nspdo);
400 printf("Points on Layer3 : %d on Layer4 : %d\n",nsddi,nsddo);
401 printf("Points on Layer5 : %d on Layer6 : %d\n",nssdi,nssdo);
402 printf("Points on all Layers: %d\n",num);
403 printf("\n ************* Init Points Finished *************\n");
406 // ------------------------------------------------------------------------
407 ///////////////////////////////////////////////////////////
408 // Functions for sorting the fPointRecs array
409 ///////////////////////////////////////////////////////////
410 Bool_t SortZ(const AliITSRiemannFit::AliPointtl *s1,const AliITSRiemannFit::AliPointtl *s2){
411 // Z sorting function for qsort.
414 a = s1->GetZ() - s2->GetZ();
415 if(a<0.0) return kTRUE;
416 if(a>0.0) return kFALSE;
419 Bool_t SortTrack(const AliITSRiemannFit::AliPointtl *s1,const AliITSRiemannFit::AliPointtl *s2){
420 // track sorting function for qsort.
423 a = s1->GetTrack() - s2->GetTrack();
424 if(a<0.0) return kTRUE;
425 if(a>0.0) return kFALSE;
428 void hpsortTrack(AliITSRiemannFit::AliPointtl **ra,Int_t n){
430 AliITSRiemannFit::AliPointtl *rra;
434 l = ((n-1) >> 1) +1; // divide 2 + 1
438 rra = ra[--l]; // decrement first
442 if(--ir == 0){ // decrement first
450 if( j<ir && SortTrack(ra[j],ra[j+1]) ) j++;
451 if( SortTrack(rra,ra[j]) ){
462 void hpsortZ(AliITSRiemannFit::AliPointtl **ra,Int_t n){
464 AliITSRiemannFit::AliPointtl *rra;
468 l = ((n-1) >> 1) +1; // devide 2 + 1
472 rra = ra[--l]; // decrament first
476 if(--ir == 0){ // decrament first
484 if( j<ir && SortZ(ra[j],ra[j+1]) ) j++;
485 if( SortZ(rra,ra[j]) ){
496 //-----------------------------------------------------------------------
497 ////////////////////////////////////////////////////////////////////
499 ///////////////////////////////////////////////////////////////////
500 Int_t Partition(Int_t array[],Int_t left,Int_t right){
501 Int_t val = array[left];
503 Int_t rm = right + 1;
514 Int_t tempr = array[rm];
525 ///////////////////////////////////////////////////////////////////////
527 void AliITSRiemannFit::WritePoints(void) {
528 /////////////////////////////////////////////////////////////////////
529 // write the data in a file (temporary ascii)
530 /////////////////////////////////////////////////////////////////////
531 FILE *ascii= fopen("AsciiPoints.dat","w");
532 for(Int_t i=0;i<fPoints;i++) {
533 fprintf(ascii,"%d\t%d\t%f\t%f\t%f\n",fPointRecs[i]->GetLay(),
534 fPointRecs[i]->GetTrack(),fPointRecs[i]->GetX(),
535 fPointRecs[i]->GetY(),fPointRecs[i]->GetZ());
540 //-----------------------------------------------------------------------
542 void AliITSRiemannFit::ReadPoints(void) {
543 //////////////////////////////////////////////////////////////////////
544 // read the filled array
545 /////////////////////////////////////////////////////////////////////
546 hpsortTrack(fPointRecs,fPoints);
547 for(Int_t i=0;i<fPoints;i++)
548 printf("%d\t%d\t%d\t%f\t%f\t%f\t(%.0f,%.0f,%.0f)\t%.3f\t%s\n",
549 i,fPointRecs[i]->GetLay(),fPointRecs[i]->GetTrack(),
550 fPointRecs[i]->GetX(),fPointRecs[i]->GetY(),
551 fPointRecs[i]->GetZ(),fPointRecs[i]->GetOrigin()->X(),
552 fPointRecs[i]->GetOrigin()->Y(),fPointRecs[i]->GetOrigin()->Z(),
553 fPointRecs[i]->GetPt(),fPointRecs[i]->GetName());
556 //-----------------------------------------------------------------------
558 Int_t AliITSRiemannFit::SolveCubic(Double_t a,Double_t b,Double_t c,
559 Double_t &x1,Double_t &x2,Double_t &x3){
560 //////////////////////////////////////////////
561 /// Solve cubic equation:
562 /// x^3 + a*x^2 +b*x + c
564 /// returns x1 , x2 , x3
565 ////////////////////////////////////////
567 Double_t qQ = ((a*a - 3*b)/9);
568 Double_t rR = ((2*a*a*a - 9*a*b +27*c)/54);
570 Double_t aF = -2*sqrt(qQ);
572 Double_t pPI2 = TMath::Pi()*2;
574 if( rR*rR>qQ*qQ*qQ ) {
575 cout<<"\nTrack "<<"Determinant :\n\t\t No Real Solutions !!!\n"<<endl;
582 theta = TMath::ACos(rR/sqrt(qQ*qQ*qQ));
584 x1 = (aF*TMath::Cos(theta/3))-g;
585 x2 = (aF*TMath::Cos((theta+pPI2)/3))-g;
586 x3 = (aF*TMath::Cos((theta-pPI2)/3))-g;
590 //-----------------------------------------------------------------
592 void RiemannTransf(Int_t npoints,TVector3 **From,TVector3 **To) {
593 ///////////////////////////////////////////////////////////////////////
594 // This function apllies the transformation in the Riemann sphere
596 ///////////////////////////////////////////////////////////////////////
597 Float_t *rR = new Float_t[npoints];
598 Float_t *theta = new Float_t[npoints];
599 Float_t pPI2 = 2*TMath::Pi();
602 for(Int_t i=0;i<npoints;i++) {
603 rR[i] = sqrt(From[i]->X()*From[i]->X()+From[i]->Y()*From[i]->Y());
604 theta[i] = TMath::ATan2(From[i]->Y(),From[i]->X());
605 if(theta[i]<0) theta[i]+=pPI2;
606 x = rR[i]*cos(theta[i])/(1+rR[i]*rR[i]);
607 y = rR[i]*sin(theta[i])/(1+rR[i]*rR[i]);
608 z = rR[i]*rR[i]/(1+rR[i]*rR[i]);
609 To[i]->SetXYZ(x,y,z);
617 //---------------------------------------------------------------------
619 Int_t FitLinear(Int_t npoints, TVector3 **input, TVector3 **errors, Double_t omega,
620 Double_t &thu0, Double_t &thv0, Double_t &phi, TVector2 &zData, TVector3 &zError,
622 ///////////////////////////////////////////////////////////////////////
623 // Fit the points in the (z,s) plane - helix 3rd equation
625 ///////////////////////////////////////////////////////////////////////
627 //PH Double_t z[npoints],x[npoints],y[npoints],s[npoints];
628 //PH Double_t ez[npoints],ex[npoints],ey[npoints],es[npoints];
629 Double_t * z = new Double_t[npoints];
630 Double_t * x = new Double_t[npoints];
631 Double_t * y = new Double_t[npoints];
632 Double_t * s = new Double_t[npoints];
633 Double_t * ez = new Double_t[npoints];
634 Double_t * ex = new Double_t[npoints];
635 Double_t * ey = new Double_t[npoints];
636 Double_t * es = new Double_t[npoints];
637 Double_t z0=0.0,vpar=0.0,ez0=0.0,evpar=0.0, chisquare;
639 // Double_t chi=TMath::Pi()/2.0+phi;
640 Double_t chi=-TMath::Pi()-phi;
641 Double_t angold=0.0, tpang=0.0;
642 for(Int_t k = 0; k<npoints; k++) {
643 x[k] = 10.0*input[k]->X(); ex[k] = 10.0*errors[k]->X();
644 y[k] = 10.0*input[k]->Y(); ey[k] = 10.0*errors[k]->Y();
645 z[k] = 10.0*input[k]->Z(); ez[k] = 10.0*errors[k]->Z();
646 if(TMath::Abs(x[k]-thu0)<1.0e-5) { // should never happen, nor give troubles...
648 cerr<<"limit for x-x_0 "<<x[k]<<" "<<thu0<<endl;
659 Double_t ang1=TMath::ATan2((y[k]-thv0),(x[k]-thu0));
660 if( (x[k]-thu0)<0 ) {
662 tpang=ang1-TMath::Sign(TMath::Pi()*2.0,ang1);
667 if (k>0) direction+=(z[k]>z[k-1] ? 1 : -1);
668 s[k] = (ang1+chi)/omega;
669 es[k]=TMath::Sqrt(ey[k]*ey[k]+ex[k]*ex[k]/TMath::Power((x[k]-thu0),4))*TMath::Abs(s[k]);
671 if ( TMath::Abs(direction) != (npoints-1) ) {return 11;}
673 TGraphErrors *fitHist = new TGraphErrors(npoints,s,z,es,ez);
674 fitHist->Fit("pol1","qQ");
675 z0 = fitHist->GetFunction("pol1")->GetParameter(0);
676 vpar = fitHist->GetFunction("pol1")->GetParameter(1);
677 ez0 = fitHist->GetFunction("pol1")->GetParError(0);
678 evpar = fitHist->GetFunction("pol1")->GetParError(1);
679 chisquare = fitHist->GetFunction("pol1")->GetChisquare();
681 zError.SetXYZ(ez0,evpar,chisquare);
689 for(Int_t j = 0; j < npoints; j++) {
694 avs /= (Double_t)npoints;
695 avz /= (Double_t)npoints;
696 avsz /= (Double_t)npoints;
698 for(Int_t l = 0; l < npoints; l++) {
699 sigmas += (s[l]-avs)*(s[l]-avs);
700 sigmaz += (z[l]-avz)*(z[l]-avz);
702 sigmas /=(Double_t)npoints;
703 sigmaz /=(Double_t)npoints;
705 sigmas = sqrt(sigmas);
706 sigmaz = sqrt(sigmaz);
708 corrLin = (avsz-avs*avz)/(sigmas*sigmaz);
722 //-------------------------------------------------------------------
723 Int_t AliITSRiemannFit::FitHelix(Int_t tracknumber,Double_t Px,Double_t Py,Double_t Pz,Double_t& fd0,
724 Double_t& fphi,Double_t& u0, Double_t& v0, Double_t& rho,Double_t& omega, Double_t& z0,
725 Double_t& vpar,Double_t& chisql, Double_t& fCorrLin,Double_t& fFit,
726 Int_t first,Int_t second,Int_t third,Int_t fourth,Int_t fifth,Int_t sixth) {
727 ///////////////////////////////////////////////////////////////////////
728 // This function finds the helix paramenters
729 // d0 = impact parameter
730 // rho = radius of circle
733 // starting from the momentum and the outcome of
734 // the fit on the Riemann sphere (i.e. u0,v0,rho)
736 // MIND !!!! Here we assume both angular velocities be 1.0 (yes, one-dot-zero !)
739 ///////////////////////////////////////////////////////////////////////
741 // All this stuff relies on this hypothesis !!!
743 // FILE *pout=fopen("chisql.dat","a");
744 Int_t ierr = 0, ierrl=0;
747 Int_t bitlay[6]={1,1,1,1,1,1};
748 bitlay[0]*=first; bitlay[1]*=second; bitlay[2]*=third; bitlay[3]*=fourth; bitlay[4]*=fifth; bitlay[5]*=sixth;
749 fd0 = -9999; // No phisycs value
750 u0 = -9999.9999; // parameters of helix - strange value...
751 v0 = -9999.9999; // parameters of helix - strange value...
752 rho = -9999.9999; // parameters of helix -unphysical strange value...
754 const Char_t* name = 0;
758 Int_t npl[6]={0,0,0,0,0,0};
759 Double_t pP = sqrt(Px*Px+Py*Py+Pz*Pz);
760 Double_t pt = sqrt(Px*Px+Py*Py);
764 TVector3 *ori = new TVector3[iMAX];
765 TVector3 **original = new TVector3*[iMAX];
766 TVector3 *rie = new TVector3[iMAX];
767 TVector3 **riemann = new TVector3*[iMAX];
768 TVector3 *err = new TVector3[iMAX];
769 TVector3 **errors = new TVector3*[iMAX];
770 TVector3 *linerr = new TVector3[iMAX];
771 TVector3 **linerrors = new TVector3*[iMAX];
772 //PH Double_t weight[iMAX];
773 Double_t * weight = new Double_t[iMAX];
776 original[i] = &(ori[i]);
777 riemann[i] = &(rie[i]);
778 errors[i] = &(err[i]);
779 linerrors[i] = &(linerr[i]);
781 for(k =0;k<iMAX;k++) original[k]->SetXYZ(9999,9999,9999);
782 Double_t a11,a12,a13,a21,a22,a23,a31,a32,a33;
783 a11=0;a12=0;a13=0;a21=0;a22=0;a23=0;a31=0;a32=0;a33=0;
787 Double_t a,b,c,d; // cubic parameters
788 Double_t roots[3]= {0.0,0.0,0.0}; // cubic solutions
789 Double_t value = 0.0; // minimum eigenvalue
790 Double_t x1,x2,x3; // eigenvector component
791 Double_t n1,n2,n3,nr= 0;// unit eigenvector
792 Double_t radiusdm[7] = {0.3,0.4,0.7,1.49,2.38,3.91,4.36}; // beam pipe and layers radii [dm]
793 Double_t sigmaMS = 0;
794 TVector3 vVec,vVecNor;
796 // Select RecPoints belonging to the track
797 for(k =0;k<fPoints;k++){
798 if(fPointRecs[k]->GetTrack()==tracknumber) {
799 name = fPointRecs[k]->GetName();
800 pt = fPointRecs[k]->GetPt();
801 pLayer = fPointRecs[k]->GetLay();
802 Int_t ilay = pLayer-1;
803 if(npl[ilay]!=0) continue;
804 if(bitlay[ilay] == 1) {
805 original[nN]->SetXYZ(0.1*fPointRecs[k]->GetX(),0.1*fPointRecs[k]->GetY(),0.1*fPointRecs[k]->GetZ());
806 errors[nN]->SetXYZ(0.1*fPointRecs[k]->GetdX(),0.1*fPointRecs[k]->GetdY(),0.1*fPointRecs[k]->GetdZ());
807 sigmaMS = (radiusdm[pLayer]-radiusdm[0])*0.000724/pP;// beam pipe contribution
808 for(Int_t j=1;j<pLayer;j++) {
809 sigmaMS += (radiusdm[pLayer]-radiusdm[j])*0.00136/pP;
811 weight[nN] = ( 1 + original[nN]->Perp2() )*( 1+ original[nN]->Perp2() )/
812 ( errors[nN]->Perp2() + sigmaMS*sigmaMS );
813 linerrors[nN]->SetXYZ(errors[nN]->X(),errors[nN]->Y(),sqrt(errors[nN]->Z()*errors[nN]->Z()+sigmaMS*sigmaMS));
817 } //end if track==tracknumber
820 // 6 points, no more, no less
822 if(original[5]->X() == 9999 || original[6]->X() != 9999)
825 return 1; // not enough points
831 // FIT ON THE RIEMANN SPHERE FOR (x,y) PLANE
834 RiemannTransf(nN,original,riemann);
836 Double_t sumWeights = 0.0; // sum of weights factor
838 for(Int_t j=0;j<nN;j++){ // mean values for x[i],y[i],z[i]
839 xbar+=weight[j]*riemann[j]->X();
840 ybar+=weight[j]*riemann[j]->Y();
841 zbar+=weight[j]*riemann[j]->Z();
842 sumWeights+=weight[j];
849 for(Int_t j=0;j<nN;j++) { // Calculate the matrix elements
850 a11 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->X() - xbar);
851 a12 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->Y() - ybar);
852 a22 += weight[j]*(riemann[j]->Y() - ybar)*(riemann[j]->Y() - ybar);
853 a23 += weight[j]*(riemann[j]->Y() - ybar)*(riemann[j]->Z() - zbar);
854 a13 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->Z() - zbar);
855 a33 += weight[j]*(riemann[j]->Z() - zbar)*(riemann[j]->Z() - zbar);
868 // ************** Determinant parameters ********************
869 // n.b. simplifications done keeping in mind symmetry of A
873 c = (a11*(a22+a33)+a33*a22-a12*a21-a13*a31-a23*a32);
874 d = (a31*a22*a13+(a12*a21-a11*a22)*a33-2.0*a23*a13*a12+a11*a23*a32);
876 // ************** Find the 3 eigenvalues *************************
877 Int_t checkCubic = SolveCubic(b,c,d,roots[0],roots[1],roots[2]);
880 printf("Track %d Has no real solution continuing ...\n",tracknumber);
885 // **************** Find the lowest eigenvalue *****************
886 if(roots[0]<=roots[1] && roots[0]<=roots[2]) value = roots[0];
887 if(roots[1]<=roots[0] && roots[1]<=roots[2]) value = roots[1];
888 if(roots[2]<=roots[0] && roots[2]<=roots[1]) value = roots[2];
890 // ************ Eigenvector relative to value **************
892 x2 = (a33*a21-a23*a31-value*a21)/(a22*a31-a32*a21-value*a31);
893 x1 = (value-a33-a32*x2)/a31;
894 vVec.SetXYZ(x1,x2,x3);
895 vVecNor = vVec.Unit();
899 nr = -n1*xbar-n2*ybar-n3*zbar;
901 u0 = -0.5*n1/(nr+n3);
902 v0 = -0.5*n2/(nr+n3);
903 rho = sqrt((n1*n1 + n2*n2 -4*nr*(nr+n3))/(4*(nr+n3)*(nr+n3)));
906 fFit += 10.*TMath::Abs(sqrt((original[0]->X()-u0)*(original[0]->X()-u0)+(original[0]->Y()-v0)*(original[0]->Y()-v0))-rho);
907 fFit += 10.*TMath::Abs(sqrt((original[1]->X()-u0)*(original[1]->X()-u0)+(original[1]->Y()-v0)*(original[1]->Y()-v0))-rho);
908 fFit += 10.*TMath::Abs(sqrt((original[2]->X()-u0)*(original[2]->X()-u0)+(original[2]->Y()-v0)*(original[2]->Y()-v0))-rho);
909 fFit += 10.*TMath::Abs(sqrt((original[3]->X()-u0)*(original[3]->X()-u0)+(original[3]->Y()-v0)*(original[3]->Y()-v0))-rho);
910 fFit += 10.*TMath::Abs(sqrt((original[4]->X()-u0)*(original[4]->X()-u0)+(original[4]->Y()-v0)*(original[4]->Y()-v0))-rho);
911 fFit += 10.*TMath::Abs(sqrt((original[5]->X()-u0)*(original[5]->X()-u0)+(original[5]->Y()-v0)*(original[5]->Y()-v0))-rho);
913 fd0 = 100000.*(TMath::Sqrt(u0*u0+v0*v0)-rho); // transverse impact parameter in microns
914 fphi = TMath::ATan2(v0,u0);
916 //**************************************************************************
917 // LINEAR FIT IN (z,s) PLANE: z = zData.X() + zData.Y()*s
918 // strictly linear (no approximation)
919 //**************************************************************************
921 ////////////////////////////////////////////////////////////////////////////////////////////////////////////
923 // REMEMBER, HERE STILL LENGHTS IN DM'S FOR ___INPUT___ BUT zDATA PARAMETERS ARE RETURNED IN CM'S //
924 // rho, u0, v0 parameters converted right now to cm's... it's a mess, I'll take care, sometimes... //
926 ////////////////////////////////////////////////////////////////////////////////////////////////////////////
931 ierrl=FitLinear(nN,original,linerrors,omega,u0,v0,fphi,zData,zError,corrLin);
933 // fprintf(pout,"%f \n",chisql);
937 ierr = (ierrl > ierr ? ierrl : ierr);
942 Int_t AliITSRiemannFit::FitHelix(Int_t NPoints, TVector3** fPointRecs,TVector3** fPointRecErrors,Float_t& f1, Float_t& f2, Float_t& f3) {
944 ///////////////////////////////////////////////////////////////////////
945 // This function finds the helix parameters
946 // d0 = impact parameter
947 // rho = radius of circle
950 // starting from the momentum and the outcome of
951 // the fit on the Riemann sphere (i.e. u0,v0,rho)
953 // MIND !!!! Here we assume both angular velocities be 1.0e-2 (yes, 0.01 !)
956 // Also linear fit in (z,s) is performed, so it's 3-D !
957 // z0 and vpar are calculated (intercept and z-component of velocity, but
958 // in units... you guess.
961 // Values calculated in addition:
963 // - transverse impact parameter fd0
964 // - sum of residuals in (x,y) plane fFit
965 // - chisquare of linear fit chisql
966 // - correlation coefficient fCorrLin
972 ///////////////////////////////////////////////////////////////////////
974 // All this stuff relies on this hypothesis !!!
976 Int_t ierr = 0, ierrl=0;
977 const Double_t kOmega = 1.0e-2;
982 Double_t fd0 = -9999; // fake values
983 Double_t u0 = -9999.9999; // for eventual
984 Double_t v0 = -9999.9999; // debugging
985 Double_t rho = -9999.9999; //
986 Double_t fphi, fFit, chisql, z0, vpar, fCorrLin;
989 // This info is no more there... to be re-considered... maybe
991 // Double_t pP = sqrt(Px*Px+Py*Py+Pz*Pz);
992 // Double_t pt = sqrt(Px*Px+Py*Py);
997 TVector3 *ori = new TVector3[NPoints];
998 TVector3 **original = new TVector3*[NPoints];
999 TVector3 *rie = new TVector3[NPoints];
1000 TVector3 **riemann = new TVector3*[NPoints];
1001 TVector3 *err = new TVector3[NPoints];
1002 TVector3 **errors = new TVector3*[NPoints];
1003 TVector3 *linerr = new TVector3[NPoints];
1004 TVector3 **linerrors = new TVector3*[NPoints];
1005 Double_t * weight = new Double_t[NPoints];
1007 for(Int_t i=0; i<NPoints; i++){
1009 original[i] = &(ori[i]);
1010 riemann[i] = &(rie[i]);
1011 errors[i] = &(err[i]);
1012 linerrors[i] = &(linerr[i]);
1014 original[i]->SetXYZ(9999,9999,9999);
1018 // Riemann fit parameters
1020 Double_t a11,a12,a13,a21,a22,a23,a31,a32,a33;
1021 a11=0;a12=0;a13=0;a21=0;a22=0;a23=0;a31=0;a32=0;a33=0;
1026 Double_t a,b,c,d; // cubic parameters
1027 Double_t roots[3]= {0.0,0.0,0.0}; // cubic solutions
1028 Double_t value = 0.0; // minimum eigenvalue
1029 Double_t x1,x2,x3; // eigenvector component
1030 Double_t n1,n2,n3,nr= 0; // unit eigenvector
1031 TVector3 vVec,vVecNor;
1033 for (Int_t ip=0; ip<NPoints; ip++) {
1034 original[ip]->SetXYZ(0.1*fPointRecs[ip]->X(),0.1*fPointRecs[ip]->Y(),0.1*fPointRecs[ip]->Z());
1036 errors[ip]->SetXYZ(0.1*fPointRecErrors[ip]->X(),0.1*fPointRecErrors[ip]->Y(),0.1*fPointRecErrors[ip]->Z());
1037 weight[ip] = (1+original[ip]->Perp2())*(1+original[ip]->Perp2())/(errors[ip]->Perp2());
1038 linerrors[ip]->SetXYZ(errors[ip]->X(),errors[ip]->Y(),errors[ip]->Z());
1044 // FIT ON THE RIEMANN SPHERE FOR (x,y) PLANE
1047 RiemannTransf(NPoints,original,riemann);
1049 Double_t sumWeights = 0.0; // sum of weights factor
1051 for(Int_t j=0;j<NPoints;j++){ // mean values for x[i],y[i],z[i]
1052 xbar+=weight[j]*riemann[j]->X();
1053 ybar+=weight[j]*riemann[j]->Y();
1054 zbar+=weight[j]*riemann[j]->Z();
1055 sumWeights+=weight[j];
1062 for(Int_t j=0;j<NPoints;j++) { // Calculate the matrix elements
1063 a11 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->X() - xbar);
1064 a12 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->Y() - ybar);
1065 a22 += weight[j]*(riemann[j]->Y() - ybar)*(riemann[j]->Y() - ybar);
1066 a23 += weight[j]*(riemann[j]->Y() - ybar)*(riemann[j]->Z() - zbar);
1067 a13 += weight[j]*(riemann[j]->X() - xbar)*(riemann[j]->Z() - zbar);
1068 a33 += weight[j]*(riemann[j]->Z() - zbar)*(riemann[j]->Z() - zbar);
1071 // this doesn't seem to work...
1073 // a11 /= sumWeights;
1074 // a12 /= sumWeights;
1075 // a22 /= sumWeights;
1076 // a23 /= sumWeights;
1077 // a13 /= sumWeights;
1078 // a33 /= sumWeights;
1090 // ************** Determinant parameters ********************
1091 // n.b. simplifications done keeping in mind symmetry of A
1095 c = (a11*(a22+a33)+a33*a22-a12*a21-a13*a31-a23*a32);
1096 d = (a31*a22*a13+(a12*a21-a11*a22)*a33-2.0*a23*a13*a12+a11*a23*a32);
1098 // ************** Find the 3 eigenvalues *************************
1099 Int_t checkCubic = SolveCubic(b,c,d,roots[0],roots[1],roots[2]);
1101 if(checkCubic !=1 ){
1102 printf("No real solution. Check data.\n");
1107 // **************** Find the lowest eigenvalue *****************
1108 if(roots[0]<=roots[1] && roots[0]<=roots[2]) value = roots[0];
1109 if(roots[1]<=roots[0] && roots[1]<=roots[2]) value = roots[1];
1110 if(roots[2]<=roots[0] && roots[2]<=roots[1]) value = roots[2];
1112 // ************ Eigenvector relative to value **************
1114 x2 = (a33*a21-a23*a31-value*a21)/(a22*a31-a32*a21-value*a31);
1115 x1 = (value-a33-a32*x2)/a31;
1116 vVec.SetXYZ(x1,x2,x3);
1117 vVecNor = vVec.Unit();
1121 nr = -n1*xbar-n2*ybar-n3*zbar;
1123 u0 = -0.5*n1/(nr+n3);
1124 v0 = -0.5*n2/(nr+n3);
1125 rho = sqrt((n1*n1 + n2*n2 -4*nr*(nr+n3))/(4*(nr+n3)*(nr+n3)));
1129 for (Int_t i=0; i<NPoints; i++) {
1130 fFit += 10.*TMath::Abs(sqrt((original[i]->X()-u0)*(original[i]->X()-u0)+(original[i]->Y()-v0)*(original[i]->Y()-v0))-rho);
1132 fd0 = 100000.*(TMath::Sqrt(u0*u0+v0*v0)-rho); // transverse impact parameter in microns
1133 fphi = TMath::ATan2(v0,u0);
1135 //**************************************************************************
1136 // LINEAR FIT IN (z,s) PLANE: z = zData.X() + zData.Y()*s
1137 // strictly linear (no approximation)
1138 //**************************************************************************
1140 ////////////////////////////////////////////////////////////////////////////////////////////////////////////
1142 // REMEMBER, HERE STILL LENGHTS IN DM'S FOR ___INPUT___ BUT zDATA PARAMETERS ARE RETURNED IN CM'S //
1143 // rho, u0, v0 parameters converted right now to cm's... it's a mess, I'll take care, sometimes... //
1145 ////////////////////////////////////////////////////////////////////////////////////////////////////////////
1151 ierrl=LinearFit(NPoints,original,linerrors,kOmega,u0,v0,fphi,zData,zError,corrLin);
1152 if(ierrl==33) return 0;
1154 // fprintf(pout,"%f \n",chisql);
1158 ierr = (ierrl > ierr ? ierrl : ierr);
1163 f2=vpar/(kOmega*TMath::Abs(rho));
1179 //____________________________________________________________
1181 Int_t AliITSRiemannFit::LinearFit(Int_t npoints, TVector3 **input,
1182 TVector3 **errors, Double_t omega,
1183 Double_t &thu0, Double_t &thv0, Double_t &phi,TVector2 &zData, TVector3 &zError,
1185 ///////////////////////////////////////////////////////////////////////
1186 // Fit the points in the (z,s) plane - helix 3rd equation
1188 ///////////////////////////////////////////////////////////////////////
1192 //PH Double_t z[npoints],x[npoints],y[npoints],s[npoints];
1193 //PH Double_t ez[npoints],ex[npoints],ey[npoints],es[npoints];
1194 Double_t * z = new Double_t[npoints];
1195 Double_t * x = new Double_t[npoints];
1196 Double_t * y = new Double_t[npoints];
1197 Double_t * s = new Double_t[npoints];
1198 Double_t * ez = new Double_t[npoints];
1199 Double_t * ex = new Double_t[npoints];
1200 Double_t * ey = new Double_t[npoints];
1201 Double_t * es = new Double_t[npoints];
1202 Double_t z0=0.0,vpar=0.0,ez0=0.0,evpar=0.0, chisquare;
1205 // Double_t chi=TMath::Pi()/2.0+phi;
1206 Double_t chi=-TMath::Pi()-phi;
1207 Double_t angold=0.0, tpang=0.0;
1208 for(Int_t k = 0; k<npoints; k++) {
1209 x[k] = 10.0*input[k]->X(); ex[k] = 10.0*errors[k]->X();
1210 y[k] = 10.0*input[k]->Y(); ey[k] = 10.0*errors[k]->Y();
1211 z[k] = 10.0*input[k]->Z(); ez[k] = 10.0*errors[k]->Z();
1212 if(TMath::Abs(x[k]-thu0)<1.0e-5) { // should never happen, nor give troubles...
1214 cerr<<"limit for x-x_0 "<<x[k]<<" "<<thu0<<endl;
1225 Double_t ang1=TMath::ATan2((y[k]-thv0),(x[k]-thu0));
1226 if( (x[k]-thu0)<0 ) {
1227 if (ang1*angold<0) {
1228 tpang=ang1-TMath::Sign(TMath::Pi()*2.0,ang1);
1233 if (k>0) direction+=(z[k]>z[k-1] ? 1 : -1);
1234 s[k] = (ang1+chi)/omega;
1235 es[k]=TMath::Sqrt(ey[k]*ey[k]+ex[k]*ex[k]/TMath::Power((x[k]-thu0),4))*TMath::Abs(s[k]);
1237 if ( TMath::Abs(direction) != (npoints-1) ) {return 11;}
1239 // if(s[0]>-636 && s[0]<-625) return 33;
1241 TGraph* fitHist = new TGraph(npoints,s,z);
1242 TF1* f1 = new TF1("f1",Fitfunction,-100,100,2);
1244 f1->SetParameter(0,1);
1245 f1->SetParameter(1,1);
1246 f1->SetLineColor(2);
1247 fitHist->Fit(f1,"qQ");
1249 z0 = f1->GetParameter(0);
1250 vpar = f1->GetParameter(1);
1251 ez0 = f1->GetParError(0);
1252 evpar= f1->GetParError(1);
1253 chisquare=f1->GetChisquare();
1255 zError.SetXYZ(ez0,evpar,chisquare);
1263 for(Int_t j = 0; j < npoints; j++) {
1268 avs /= (Double_t)npoints;
1269 avz /= (Double_t)npoints;
1270 avsz /= (Double_t)npoints;
1272 for(Int_t l = 0; l < npoints; l++) {
1273 sigmas += (s[l]-avs)*(s[l]-avs);
1274 sigmaz += (z[l]-avz)*(z[l]-avz);
1276 sigmas /=(Double_t)npoints;
1277 sigmaz /=(Double_t)npoints;
1279 sigmas = sqrt(sigmas);
1280 sigmaz = sqrt(sigmaz);
1282 corrLin = (avsz-avs*avz)/(sigmas*sigmaz);
1294 delete f1; delete fitHist;
1299 //_______________________________________________________
1301 Double_t AliITSRiemannFit::Fitfunction(Double_t *x, Double_t* par){
1302 // function used for fit
1303 return par[0]+(*x)*par[1];